Channel estimation method and system using fast fourier transforms

ABSTRACT

A low cost method and system for efficiently implementing channel estimation in a wireless communication system using any desired length of a fast Fourier transform (FFT) independent of burst type or signal structure. The hardware complexity required to perform the channel estimation to process a plurality of different burst types is reduced. Simple tail zero-padding is used when the length of FFT is extended to a desired length for more efficient computation.

CROSS REFERENCE TO RELATED APPLICATION(S)

[0001] This application claims priority from U.S. patent application No.60/460,852, filed Apr. 4, 2003, which is incorporated by reference as iffully set forth.

FIELD OF INVENTION

[0002] This invention generally relates to channel estimation inwireless communications. In particular, the invention relates to lowcost channel estimation using fast Fourier transform (FFT).

BACKGROUND

[0003] In code division multiple access (CDMA) communication systems,multiple communications may be simultaneously sent over a sharedfrequency spectrum. Each communication is distinguished by the code usedto transmit the communication.

[0004] In one type of CDMA communication system, the shared spectrum istime divided into frames having a predetermined number of time slots,such as fifteen time slots. This system is referred to as a hybridCDMA/time division multiple access (TDMA) communication systems. Inanother type of CDMA system, uplink and downlink communications arerestricted to particular time slots. This system is referred to as atime division duplex (TDD) communication system.

[0005] In a typical TDD/CDMA communication system, communication data issent using communication bursts. FIG. 1 illustrates a communicationburst 16 having a midamble 20, a guard period 18 and two data fields 22,24. The data fields 22, 24 carry the data of the communication burst 16.The guard period 18 separates the communication bursts 16 to allow for adifference in arrival times of bursts transmitted from differenttransmitters. The midamble 20 separates the two data fields 22, 24 andhas a known training sequence used to estimate the channel that thecommunication burst 16 experiences. Using the estimated channelresponse, data from the data fields 22, 24 is recovered at a receiver.For the third generation partnership (3GPP) wideband CDMA (W-CDMA),based on the burst type, the basic midamble codes used to generatemidamble bursts have differing lengths. To illustrate, the basicmidamble code for burst type I has 456 chips while burst type II has 192chips.

[0006] FFT is a powerful tool for efficient implementation of a wirelesscommunications receiver. One drawback with FFT implementations is thatthey are limited to operating on fields with a predetermined length.

[0007] It is desirable to have a channel estimator using an FFT enginethat has the capabilities to handle channel estimation for various typesof bursts.

SUMMARY OF THE INVENTION

[0008] In a wireless communication system, channel estimation isperformed by receiving reference signals having different lengths,processing the reference signals using a fast Fourier transform (FFT),and extending the FFT to a desired length L for more efficientcomputation. The FFT is extended to the length L to process a pluralityof different burst types associated with the reference signals.

BRIEF DESCRIPTION OF THE DRAWINGS

[0009] A more detailed understanding of the invention may be had fromthe following description of a preferred example, given by way ofexample and to be understood in conjunction with the accompanyingdrawing wherein:

[0010]FIG. 1 is an illustration of a communication burst.

[0011]FIG. 2 is a simplified diagram of a transmitter and a receiverusing channel estimation.

[0012]FIG. 3 is a system block diagram illustrating the process forimplementing channel estimation in accordance with a preferredembodiment of the present invention.

[0013]FIG. 4 is a flow chart illustrating the process to calculate F(r)and F(m) by extended FFT and divide them element-to-element.

[0014]FIG. 5 is a flow chart illustrating the process to compute F(H*)by the extended FFT and then conjugate and scale the result.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT(S)

[0015] Although the preferred embodiments are described in conjunctionwith a preferred TDD/CDMA or TDMA/CDMA communication system, someaspects are also applicable to CDMA systems in general, includingTD-SCDMA. However, the invention in its broad form is envisaged to beapplicable to other systems of transmission also, without limitation.

[0016] Hereafter, a wireless transmit/receive unit (WTRU) includes butis not limited to a user equipment, mobile station, fixed or mobilesubscriber unit, pager, or any other type of device capable of operatingin a wireless environment. When referred to hereafter, a base stationincludes but is not limited to a base station, Node-B, site controller,access point or other interfacing device in a wireless environment.

[0017]FIG. 2 illustrates an embodiment of channel estimation as used ina wireless communication system operating in accordance with the presentinvention. A transmitter 30 and a receiver 32 communicate with eachother via a wireless radio air interface 38. The transmitter 30 may belocated at a WTRU or at a base station. The receiver 32 may be locatedat the WTRU and/or the base station.

[0018] Data symbols to be transmitted to the receiver 32 are processedby a modulation and spreading device 34 at the transmitter 30. Themodulation and spreading device 34 spreads the data with the codes andat a spreading factor(s) assigned to the communication(s) carrying thedata. The communication(s) are radiated by an antenna 36 or antennaarray of the transmitter 30 through the wireless radio interface 38.

[0019] At the receiver 32, the communication(s), possibly along withother transmitters' communications, are received at an antenna 40 orantenna array of the transmitter 30. The received signal is sampled by asampling device 42, such as at the chip rate or at a multiple of thechip rate, to produce a received vector. The received vector isprocessed by a channel estimation device 46 to estimate the channelimpulse responses for the received communications. The channelestimation device 46 uses a training sequence in the receivedcommunication to estimate the channel experienced by each communication.A data detection device 44, such as a joint detection device, uses thecode(s) of the received communication(s) and the estimated impulseresponse(s) to estimate soft symbols of the spread data.

[0020] The following is a description of an exemplary process forchannel estimation with a single length FFT.

[0021] For channel estimation, the received signal r can be expressed asthe circular convolution of two sequences, the midamble sequence, m andthe channel impulse response, h by

r=m{circle over (×)}h   Equation (1)

[0022] where {circle over (×)} is defined as the circular convolutionoperator.

[0023] In frequency domain, the circular convolution of two signalsbecomes a product of frequency responses of two signals, and thefrequency response of the resulting output signal becomes

R=M·H   Equation (2)

[0024] where R is the FFT of time domain signal r, M is the FFT ofmidamble sequence m and H is the FFT of channel impulse response h. Inshort they are expressed by R=F(r), M=F(m) and H=F(h) where F( ) isdefined as the operator for forward FFT and F⁻¹( ) is defined as theoperator for inverse FFT. The “underscore” indicates that the signal isa vector.

[0025] To obtain the estimated channel response, first H is calculatedby $\begin{matrix}{\underset{\_}{H} = \frac{\underset{\_}{R}}{\underset{\_}{M}}} & {{Equation}\quad (3)}\end{matrix}$

[0026] where R/M is the element-to-element division of the correspondingtwo FFT sequences. The channel impulse response can be estimated byinverse FFT of H by

h=F ⁻¹(H)   Equation (4)

[0027] The whole process can be summarized in one single equation by

h=F ⁻¹(F(r)/F(m))   Equation (5)

[0028] F(r)/F(m) in Equation (5) denotes the element-to-element divisionof FFT sequences F(r) and F(m). Note that the forward and inverse FFTare exchangeable in the following form as illustrated for vector x:$\begin{matrix}{{F^{- 1}\left( \underset{\_}{x} \right)} = {\frac{1}{P}\left( {F\left( {\underset{\_}{x}}^{*} \right)} \right)^{*}}} & {{Equation}\quad (6)}\end{matrix}$

[0029] where P is the length of FFT.

[0030] To enable a single-length FFT, the FFT operations used forchannel estimation as shown in Equation (5) should be extended to alonger desired length. In the preferred embodiment, the length ofextended FFT should be at least long enough to account for all bursttypes including burst types 1, 2 and 3 so that FFTs in Equation (5) willnot depend on the burst type, although in other systems andimplementations the length may vary. To extend a FFT to any longerproper length L, a chirp transform algorithm (CTA) is used to computeF(r) and F(m) in Equation (5) by an extended FFT. The inverse FFT (IFFT)for F⁻¹(H) in Equation (4) can be implemented by the forward FFT. Thiscan be done by performing FFT on the conjugate signal of H and thentaking conjugate on the resulting FFT output and scaling it properly asshown in Equation (6). CTA is used to compute F(H*) by extended FFT.

[0031] The procedure for extended FFT and efficient channel estimationis described as follows:

[0032] There are two stages to be performed. The first stage calculatesF(r) and F(m) by extended FFT and divides them element-to-element. Thesecond stage computes F(H*) by the extended FFT and then conjugates andscales the result. For the following discussions, let P denote theoriginal length of FFT and L be the extended length of FFT using tailzero-padding. The original lengths of FFT for example, are P=456 andP=192 for burst types 1/3 and 2 respectively.

[0033]FIG. 3 is a block diagram of a system 300 including means forperforming stages 1 and 2. For stage 1, an element-to-elementmultipliers 305A, 305B multiply the sequences m and r by chirp waveformW^(n2/2) for n=0, 1, 2, . . . , P−1 where P=456 for burst types 1/3 orP=192 for burst type 2 and $W = {^{{- j}\quad \frac{2\pi}{P}}.}$

[0034] In this context, chirp waveform is referred to as the waveformgenerated by $W^{\frac{n^{2}}{2}},$

[0035] n=0, 1, 2, . . . , P−1. The resulting sequences are denoted asm_(W) and r_(W) respectively. A chirp sequence v is created such thatv=W^(−(n−P+1)2/2) for n=0, 1, 2, . . . , 2P−2. Chirp sequence isreferred to the modified sequence based on a chirp waveform generated by$W^{- \frac{{({n - P + 1})}^{2}}{2}},$

[0036] n=0, 1, 2, . . . , 2P-2. Chirp sequence is different from chirpwaveform with a shift in index n and with a longer waveform length. Thechirp transform algorithm refers to the entire process that performs theoriginal FFT with extended FFT, in which the chirp waveform and chirpsequence are used to transform signals in a proper format suitable forprocessing.

[0037] The sequences m_(W), r_(W) and v are processed by zero padding310A, 310B, 310C in the tail until the length of the sequences achievesL. Denote the resulting sequences as m_(W,Z), r_(W,Z and v) _(Z).L-point FFTs 315,A, 315B, 315C are implemented on m_(W,Z), r_(W,Z) andv_(Z) each such that F(m_(W,Z)), F(r_(W,Z)) and F(v_(Z)).Element-to-element multipliers 320A, 320B multiply the FFT of m_(W,Z)and r_(W,Z) each with FFT of v_(Z) such that the products are F(m_(W,Z))F(v_(Z)) and F(r_(W,Z))·F(v_(Z)) respectively. L-point inverse FFTs(IFFTs) 325A, 325B are implemented on the outputs of multipliers 320A,320B such that F⁻¹(F(m_(W,Z))·F(v_(Z))) and F⁻¹(F(r_(W,Z)) F(v_(Z)))respectively. An element-to-element divider 330 divides the outputs ofL-point IFFTs 325A, 325B and denotes the result as H 335 such that$\underset{\_}{H} = {\frac{F^{- 1}\left( {{F\left( {\underset{\_}{r}}_{W,Z} \right)} \cdot {F\left( {\underset{\_}{v}}_{Z} \right)}} \right.}{F^{- 1}\left( {{F\left( {\underset{\_}{m}}_{W,Z} \right)} \cdot {F\left( {\underset{\_}{v}}_{Z} \right)}} \right.}.}$

[0038] Note that only the first P elements of sequence H are computedand used.

[0039] Still referring to FIG. 3, for stage 2, conjugate device 340conjugates the sequence H that was obtained in the final step of stage1. Element-to-element multiplier 345 multiplies the conjugate sequenceH* by chirp waveform W^(n2/2) for n=0, 1, 2, . . . , P−1. The result isdenoted as H*_(W). Zero padding 350 zero pads the conjugate sequencesH*_(W) in the tail until the length of the sequence achieves length L.The resulting sequence is denoted as H*_(W,Z). An L-point FFT 355 isperformed on H*_(W,Z). Element-to-element multiplier 360 multiplies theFFT of H*_(W,Z) by FFT of zero-padded chirp sequence v_(Z) such that theproduct is F(H*_(W,Z))·F(v_(Z)). An L-point IFFT 365 is implemented onthe output of multiplier 360 resulting F(H*_(W,Z))·F(v_(Z)).Element-to-element multiplier 370 multiplies the sequenceF(H*_(W,Z))·F(v_(Z)) by chirp waveform W^(n2/2) for n=0, 1, 2, . . . ,P−1. Note that only the first P elements are calculated and used. Theoutput of multiplier 370 is conjugated by conjugate device 375 and theresult is scaled by scaling device 380 by factor $\frac{1}{P}$

[0040] to obtain the estimated channel response.

[0041] Referring to FIG. 4, the procedure for stage 1 by the extendedFFT is described as follows:

[0042] In step 405, element-to-element, multiply the sequences m and rby chirp waveform W^(n2/2) for n=0, 1, 2, . . . , P−1 where P=456 forburst types 1/3 or P=192 for burst type 2. Denote the resultingsequences as m_(W) and r_(W) respectively.

[0043] In step 410, create a chirp sequence v such thatv=W^(−(n−P+1)2/2) for n=0, 1, 2, . . . , 2P−2.

[0044] In step 415, zero pad the sequences m_(W), r_(W) and v in thetail until the length of the sequences achieves L. Denote the resultingsequences as m_(W,Z), r_(W,Z) and v_(Z) .

[0045] In step 420, perform L-point FFT on m_(W,Z), r_(W,Z) and v_(Z)each such that F(m_(W,Z)), F(r_(W,Z)) and F(v_(Z)).

[0046] In step 425, element-to-element multiply the FFT of m_(W,Z) andr_(W,Z) each with FFT of v_(Z) such that the products areF(m_(W,Z))·F(v_(Z)) and F(r_(W,Z))·F(v_(Z)) respectively.

[0047] In step 430, an L-point inverse FFT is performed onF(m_(W,Z))·F(v_(Z)) and F(r_(W,Z))·F(v_(Z)) such thatF⁻¹(F(m_(W,Z))·F(v_(Z))) and F⁻¹(F(r_(W,Z))·F(v_(Z))) respectively.

[0048] In step 435, element-to-element divide F⁻¹(F(m_(W,Z))·F(v_(Z)))by F⁻¹(F(r_(W,Z))·F(v_(Z))) and denote the result as H such that$\underset{\_}{H} = {\frac{F^{- 1}\left( {{F\left( {\underset{\_}{r}}_{W,Z} \right)} \cdot {F\left( {\underset{\_}{v}}_{Z} \right)}} \right.}{F^{- 1}\left( {{F\left( {\underset{\_}{m}}_{W,Z} \right)} \cdot {F\left( {\underset{\_}{v}}_{Z} \right)}} \right.}.}$

[0049] Note that only the first P elements of sequence H are computedand used.

[0050] Note that basic midamble code is fixed in a cell and the chirpsequence is constant once it is generated, the computation ofF⁻¹(F(m_(W,Z))·F(v_(Z))) can be pre-computed once and for all and storedfor each cell.

[0051] Referring to FIG. 5, the procedure for stage 2 is to computeF(H*) by extended FFT and conjugate and scale the result is described asfollows:

[0052] In step 505, conjugate the sequence H that was obtained in thefinal step of stage 1 (step 435).

[0053] In step 510, element-to-element multiply the conjugate sequenceH* by chirp waveform W^(n2/2) for n=0, 1, 2, . . . , P−1. Denote theresult as H*_(W).

[0054] In step 515, zero pad the conjugate sequences H*_(W) in the tailuntil the length of the sequence achieves L. Denote the resultingsequence as H*_(W,Z).

[0055] In step 520, perform L-point FFT on H*_(W,Z).

[0056] In step 525, element-to-element multiply the FFT of H*_(W,Z) byFFT of zero-padded chirp sequence v_(Z) such that the product isF(H*_(W,Z))·F(v_(Z)).

[0057] In step 530, perform L-point inverse FFT on F(H*_(W,Z))·F(v_(Z)).

[0058] In step 535, element-to-element multiply the sequenceF⁻¹(F(H*_(W,Z))·F(v_(Z))) by chirp waveform W^(n2/2) for N=0, 1, 2, . .. , P−1. Note that only the first P elements are calculated and used.

[0059] In step 540, conjugate the result in step 535.

[0060] In step 545, scale the result in step 540 by factor $\frac{1}{P}$

[0061] to obtain the estimated channel response.

[0062] The above method of extended FFT using simple zero padding forchannel estimation is very cost efficient in terms of hardwarecomplexity. High computational efficiency is also achievable when theextended FFT length is optimized for specific computing algorithms suchas a prime factor algorithm (PFA) or Radix-2 algorithm.

[0063] While this invention has been particularly shown and describedwith reference to preferred embodiments, it will be understood by thoseskilled in the art that various changes in form and details may be madetherein without departing from the scope of the invention describedhereinabove.

What is claimed is:
 1. In a wireless communication system, a method ofperforming channel estimation, the method comprising: (a) receivingreference signals having different lengths; (b) processing the referencesignals using a fast Fourier transform (FFT); and (c) extending the FFTto a desired length L for more efficient computation.
 2. The method ofclaim 1 wherein the FFT is extended to the length L to process aplurality of different burst types associated with the referencesignals.
 3. In a wireless communication system, a method of performingchannel estimation, the method comprising: (a) receiving a time domainsignal r; (b) multiplying, element-to-element, the sequences m and r bya chirp waveform, the chirp waveform being based on the length of theFFT and denoting the resulting sequences as m_(W) and r_(W)respectively, where m is a midamble sequence; and (c) creating a chirpsequence v based on the chirp waveform.
 4. The method of claim 3 whereinthe chirp waveform is W^(n2/2) for n=0,1,2, . . . ,P−1 where P=456 forburst types 1/3 or P=192 for burst type 2, and$W = ^{{- j}\quad \frac{2\pi}{P}}$


5. The method of claim 4 wherein the chirp sequence v=W^(−(n−P+1)2/2)for n=0,1,2, . . . ,2P−2.
 6. A wireless communication system forperforming channel estimation, the system comprising: (a) means forreceiving reference signals having different lengths; (b) means forprocessing the reference signals using a fast Fourier transform (FFT);and (c) means for extending the FFT to a desired length L for moreefficient computation.
 7. The system of claim 6 wherein the FFT isextended to the length L to process a plurality of different burst typesassociated with the reference signals.
 8. A wireless communicationsystem for performing channel estimation, the system comprising: (a)means for receiving a time domain signal r; (b) means for multiplying,element-to-element, the sequences m and r by a chirp waveform, the chirpwaveform being based on the length of the FFT and denoting the resultingsequences as m_(W) and r_(W) respectively, where m is a midamblesequence; and (c) means for creating a chirp sequence v based on thechirp waveform.
 9. The system of claim 8 wherein the chirp waveform isW^(n2/2) for n=0,1,2, . . . ,P−1 where P=456 for burst types 1/3 orP=192 for burst type 2, and $W = {^{{- j}\frac{2\pi}{P}}.}$


10. The system of claim 9 wherein the chirp sequence v=W^(−(n−P+1)2/2)for n=0,1,2, . . . ,2P−2.
 11. A wireless transmit/receive unit (WTRU)for performing channel estimation, the WTRU comprising: (a) means forreceiving reference signals having different lengths; (b) means forprocessing the reference signals using a fast Fourier transform (FFT);and (c) means for extending the FFT to a desired length L for moreefficient computation.
 12. The WTRU of claim 11 wherein the FFT isextended to the length L to process a plurality of different burst typesassociated with the reference signals.
 13. A wireless transmit/receiveunit (WTRU) for performing channel estimation, the WTRU comprising: (a)means for receiving a time domain signal r; (b) means for multiplyingelement-to-element the sequences m and r by a chirp waveform, the chirpwaveform being based on the length of the FFT and denoting the resultingsequences as m_(W) and r_(W) respectively, where m is a midamblesequence; and (c) means for creating a chirp sequence v based on thechirp waveform.
 14. The WTRU of claim 13 wherein the chirp waveform isW^(n2/2) for n=0,1,2, . . . ,P−1 where P=456 for burst types 1/3 orP=192 for burst type 2, and $W = {^{{- j}\frac{2\pi}{P}}.}$


15. The WTRU of claim 14 wherein the chirp sequence v=W^(−(n−P+1)2/2)for n=0,1,2, . . . ,2P−2.
 16. A base station (BS) for performing channelestimation, the BS comprising: (a) means for receiving reference signalshaving different lengths; (b) means for processing the reference signalsusing a fast Fourier transform (FFT); and (c) means for extending theFFT to a desired length L for more efficient computation.
 17. The BS ofclaim 16 wherein the FFT is extended to the length L to process aplurality of different burst types associated with the referencesignals.
 18. A base station (BS) for performing channel estimation, theBS comprising: (a) means for receiving a time domain signal r; (b) meansfor multiplying element-to-element the sequences m and r by a chirpwaveform, the chirp waveform being based on the length of the FFT anddenoting the resulting sequences as m_(W) and r_(W) respectively, wherem is a midamble sequence; and (c) means for creating a chirp sequence vbased on the chirp waveform.
 19. The BS of claim 18 wherein the chirpwaveform is W^(n2/2) for n=0, 1, 2, . . . , 2P−1 where P=456 for bursttypes 1/3 or P=192 for burst type 2, and$W = {^{{- j}\frac{2\pi}{P}}.}$


20. The BS of claim 19 wherein the chirp sequence v=W^(−(n−P+1)2/2) forn=0, 1, 2, . . . , 2P−2.
 21. In a wireless communication system, amethod for performing channel estimation, the method comprising: (a)receiving a time domain signal r; (b) expressing r=m{circle over (×)}hin the frequency domain, resulting in an output signal R=M·H where m isa midamble sequence, h is a channel impulse response, {circle over (×)}is a circular convolution operator, R is the fast Fourier transform(FFT) of time domain signal r, M is the FFT of midamble sequence m, andH is the FFT of channel impulse response h, and R=F(r), M=F(m) andH=F(h) where F( ) is defined as the operator of forward or inverse FFT;(c) calculating H is calculated by dividing R by M, where R/M is theelement-to-element division of the corresponding two FFT sequences; and(d) estimating the impulse response by inverse FFT of H by calculatingh=F⁻¹(H) where F⁻¹( ) is defined as the operator of forward or inverseFFT and h=F⁻¹(F(r)/F(m)) and F(r)/F(m) denotes the element-to-elementdivision of FFT sequences F(r) and F(m).
 22. The method of claim 21wherein the forward or inverse FFT are exchangeable in the followingform:${{F^{- 1}\left( \underset{\_}{x} \right)} = {\frac{1}{P}\left( {F\left( {\underset{\_}{x}}^{*} \right)} \right)^{*}}},$

wherein P is the length of FFT.
 23. The method of claim 22 wherein theFFT sequences F(r) and F(m) are calculated by extended FFT and dividedelement-to-element, the method further comprising: (e) multiplying,element-to-element, the sequences m and r by a chirp waveform anddenoting the resulting sequences as m_(W) and r_(W) respectively; (f)creating a chirp sequence based on the chirp waveform; (g) zero paddingthe sequences m_(W), r_(W) and v in the tail until the length of thesequences achieves L, and denoting the resulting sequences as m_(W,Z),r_(W,Z) and (h) performing an L-point FFT on m_(W,Z), r_(W,Z) and v_(Z)each such that F(m_(W,Z)), F(r_(W,Z)) and F(v_(Z)); (i) multiplying,element-to-element, the FFT of m_(W,Z) and r_(W,Z) each with FFT ofv_(Z) such that the products are F(m_(W,Z))·F(v_(Z)) andF(r_(W,Z))·F(v_(Z)) respectively; (j) performing an L-point inverse onthe results in step (i) such that F⁻¹(F(m_(W,Z))·F(v_(Z))) andF⁻¹(F(r_(W,Z))·F(v_(Z))) respectively; and (k) dividing,element-to-element, the results in step (j) and denoting the result as Hsuch that$\underset{\_}{H} = \frac{F^{- 1}\left( {{F\left( {\underset{\_}{r}}_{W,Z} \right)} \cdot {F\left( {\underset{\_}{v}}_{Z} \right)}} \right.}{F^{- 1}\left( {{F\left( {\underset{\_}{m}}_{W,Z} \right)} \cdot {F\left( {\underset{\_}{v}}_{Z} \right)}} \right.}$

wherein only the first P elements of sequence H are computed and used.24. The method of claim 23 wherein F(H*) is computed by extended FFT andthe result is conjugated and scaled, the method further comprising: (l)conjugating the sequence H; (m) multiplying, element-to-element, theconjugate sequence H* by the chirp waveform and denoting the result asH*_(W); (n) zero padding the conjugate sequences H*_(W) in the tailuntil the length of the sequence achieves L, and denoting the resultingsequence as H*_(W,Z); (o) performing an L-point FFT on H*_(W,Z); (p)multiplying, element-to-element, the FFT of H*_(W,Z) by FFT ofzero-padded chirp sequence v_(Z) such that the product isF(H*_(W,Z))·F(v_(Z)); (q) performing L-point inverse FFT onF(H*_(W,Z))·F(v_(Z)); (r) multiplying, element-to-element, the sequenceF⁻¹(F(H*_(W,Z))·F(v_(Z))) by the chirp waveform; (s) conjugating theresult in step (r); and (t) scaling the result in step (s) by factor$\frac{1}{P}$

to obtain the estimated channel response.
 25. The method of claim 21wherein the FFT is extended to a proper length L to process a pluralityof different burst types by using a chirp transform algorithm (CTA) tocompute F(r) and F(m).
 26. A wireless communication system forperforming channel estimation, the system comprising: (a) means forreceiving a time domain signal r; (b) means for expressing r=m{circleover (×)}h in the frequency domain, resulting in an output signal R=M·H,where m is a midamble sequence, h is a channel impulse response, {circleover (×)} is a circular convolution operator, R is the fast Fouriertransform (FFT) of time domain signal r, M is the FFT of midamblesequence m, and H is the FFT of channel impulse response h, and R=F(r),M=F(m) and H=F(h) where F( ) is defined as the operator of forward orinverse FFT; (c) means for calculating H is calculated by dividing R byM, where R/M is the element-to-element division of the corresponding twoFFT sequences; and (d) means for estimating the impulse response byinverse FFT of H by calculating h=F⁻¹(H) where F⁻¹( ) is defined as theoperator of forward or inverse FFT and h=F⁻¹(F(r)/F(m)) and F(r)/F(m)denotes the element-to-element division of FFT sequences F(r) and F(m).27. The system of claim 26 wherein the forward or inverse FFT areexchangeable in the following form:${{F^{- 1}\left( \underset{\_}{x} \right)} = {\frac{1}{P}\left( {F\left( {\underset{\_}{x}}^{*} \right)} \right)^{*}}},$

wherein P is the length of FFT.
 28. The system of claim 27 wherein theFFT sequences F(r) and F(m) are calculated by extended FFT and dividedelement-to-element, the method further comprising: (e) means formultiplying, element-to-element, the sequences m and r by a chirpwaveform and denoting the resulting sequences as m_(W) and r_(W)respectively; (f) means for creating a chirp sequence based on the chirpwaveform; (g) means for zero padding the sequences m_(W), r_(W) and v inthe tail until the length of the sequences achieves L, and denoting theresulting sequences as m_(W,Z), r_(W,Z) and v_(Z); (h) means forperforming L-point FFT on m_(W,Z), r_(W,Z) and v_(Z) each such thatF(m_(W,Z)), F(r_(W,Z)) and F(v_(Z)); (i) means for multiplying,element-to-element, the FFT of m_(W,Z) and r_(W,Z) each with FFT ofv_(Z) such that the products are F(m_(W,Z))·F(v_(Z)) andF(r_(W,Z))·F(v_(Z)) respectively; (j) means for performing an L-pointinverse on F(m_(W,Z))·F(v_(Z)) and F(r_(W,Z)): F(v_(Z)) such thatF⁻¹(F(m_(W,Z))·F(v_(Z))) and F⁻¹(F(r_(W,Z))·F(v_(Z))) respectively; and(k) means for dividing, element-to-element, F⁻¹(F(m_(W,Z))·F(v_(Z))) byF⁻¹(F(r_(W,Z))·F(v_(Z))) and denoting the result as H such that$\underset{\_}{H} = \frac{F^{- 1}\left( {{F\left( {\underset{\_}{r}}_{W,Z} \right)} \cdot {F\left( {\underset{\_}{v}}_{Z} \right)}} \right.}{F^{- 1}\left( {{F\left( {\underset{\_}{m}}_{W,Z} \right)} \cdot {F\left( {\underset{\_}{v}}_{Z} \right)}} \right.}$

wherein only the first P elements of sequence H are computed and used.29. The system of claim 28 wherein F(H*) is computed by extended FFT andthe result is conjugated and scaled, the system further comprising: (l)means for conjugating the sequence H; (m) means for multiplying,element-to-element, the conjugate sequence H* by the chirp waveform anddenoting the result as H*_(W); (n) means for zero padding the conjugatesequences H*_(W) in the tail until the length of the sequence achievesL, and denoting the resulting sequence as H*_(W,Z); (o) means forperforming L-point FFT on H*_(W,Z); (p) means for multiplying,element-to-element, the FFT of H*_(W,Z) by FFT of zero-padded chirpsequence v_(Z) such that the product is F(H*_(W,Z))·F(v_(Z)); (q) meansfor performing an L-point inverse FFT on F(H*_(W,Z))·F(v_(Z)); (r) meansfor multiplying, element-to-element, the sequenceF⁻¹(F(H*_(W,Z))·F(v_(Z))) by the chirp waveform; (s) means forconjugating the output of means (r); and (t) means for scaling theoutput of means (s) by factor $\frac{1}{P}$

to obtain the estimated channel response.
 30. The system of claim 25wherein the FFT is extended to a proper length L to process a pluralityof different burst types by using a chirp transform algorithm (CTA) tocompute F(r) and F(m).